What is the integral of ((ln(x))^2)/((x)) ?

The integral of ((ln(x))^2)/((x)) is (ln^3(x))/3+C

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integral of ((ln(x))^2)/((x))

\int \frac{( ln ( x ) ) ^{2}}{( x )} d x

\frac{ln ^{3} ( x )}{3} + C

Solution steps

\int \frac{( ln ( x ) ) ^{2}}{x} d x

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

= \frac{u ^{3}}{3}

Substitute back

u = ln (x)

= \frac{ln ^{3} ( x )}{3}

Add a constant to the solution

= \frac{ln ^{3} ( x )}{3} + C

What is the integral of ((ln(x))^2)/((x)) ?
The integral of ((ln(x))^2)/((x)) is (ln^3(x))/3+C